Answered: Change each equation to rectangular…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter1: Variables, Expressions, And Integers

Section1.8: The Coordinate Plane

Problem 12E

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Question

Change each equation to rectangular coordinates and then graph.

r = 6 cos u

Expert Solution

Step 1

We have to change the equation in rectangular forma and graph the given polar forms:

$r = 6 \cos u$

We know the relation between polar and rectangular coordinates,

$\begin{array}{rcl} r & = & \sqrt{x^{2} + y^{2}} \\ x & = & r \cos θ \\ y & = & r \sin θ \end{array}$

So using above relation converting the equation, we get

$\begin{array}{rcl} r & = & 6 \cos u \\ r & = & 6 \times \frac{x}{r} \\ r^{2} & = & 6 x \\ {(\sqrt{x^{2} + y^{2}})}^{2} & = & 6 x \\ x^{2} + y^{2} & = & 6 x \end{array}$

Hence, converted equation in rectangular coordinate is $\begin{array}{rcl} x \end{array} \begin{array}{rcl} \end{array}$ ²+y²=6x.

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